Optimal quotients of Jacobians with toric reduction and component groups


Journal Article

© Canadian Mathematical Society 2016. Let J be a Jacobian variety with toric reduction over a local field K. Let J → E be an optimal quotient defined over K, where E is an elliptic curve. We give examples in which the functorially induced map φJ → φE on component groups of the Neron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which φJ → φE E is surjective and discuss when these criteria hold for the Jacobians of modular curves.

Full Text

Duke Authors

Cited Authors

  • Papikian, M; Rabinoff, J

Published Date

  • December 1, 2016

Published In

Volume / Issue

  • 68 / 6

Start / End Page

  • 1362 - 1381

International Standard Serial Number (ISSN)

  • 0008-414X

Digital Object Identifier (DOI)

  • 10.4153/CJM-2016-009-9

Citation Source

  • Scopus